Marek CieplakMarek CieplakInstitute of Physics, Polish Academy of Science, Institute of Physics, Polish Academy of Science,

WarsawWarsaw

Inferring genetic interaction networks Inferring genetic interaction networks from gene expression patterns in from gene expression patterns in

microarraysmicroarrays

(for Saccharomyces (for Saccharomyces cerevisiae)cerevisiae)

Microarrays arrays of spots responding to specific genes that are being expressed

fluorescently labeled mobile probes - DNA or fluorescently labeled mobile probes - DNA or mRNA – hybridize with the complementary mRNA – hybridize with the complementary templatetemplate

cDNA – complementary DNA – obtained by reverse transcription from mRNA (no introns)

glass slides, silicon chips, nylon membranes

cDNA Microarrays: single strands attached covalently at fixed locations on a solid support. The location identifies a particular gene.

medical diagnostics

incubate and then wash out unbound probesDetect by using laser confocal fluorescence

scanning

1 spot: ~ 100 μm

Oligonucleotide Oligonucleotide microarraysmicroarrays

Santa Clara, CA since 1991

first product HIV genotyping GeneChip in 1994

Light-directed, spatially addressable parallel chemical synthesisLight-directed, spatially addressable parallel chemical synthesis,,

S.P.A. FodorS.P.A. Fodor, J.L. Read, M.C. Pirrung, L. Stryer, A.T. Lu, D. Solas, , J.L. Read, M.C. Pirrung, L. Stryer, A.T. Lu, D. Solas,

Science 251, 767 (1991) Science 251, 767 (1991) 1024 spots1024 spots

Agilent Technologies

Spots with oligonucleotidic fragments (5-50 bases)

$700 mln. market in the US

semiconductor-based semiconductor-based photolithography with photolithography with photo-sensitive linkers photo-sensitive linkers

one-by-one nucleotideone-by-one nucleotide

Schena M, Shalon D, Davis RW, Brown PO. (1995). Quantitative monitoring of gene expression patterns with a complementary DNA microarray. Science. 270: 467-70.

droplets of a DNA probe sample onto a functionalized glass slide

poly-lysin or poly-amin for electrostatic adsorption

streptavidin & biotin-labeled DNA probes

Up to 10 000 spots in 1cm2

Spots with single strand cDNA (100 - 5000 bases) Spots with single strand cDNA (100 - 5000 bases)

the first had 96 spots

Spotted Spotted microarrays microarrays

Robotic spotting

Competing technology: Competing technology: high-throughput gene high-throughput gene sequencing systemssequencing systems

Assignment of function to genesThe kinds and amounts of mRNA produced by a cell tell which genes are expressed, when the cell responds to its needs and stimuli.

Gene expression is a highly complex and tightly regulated process. "on/off" switch - "volume control"

Brown: Studies of anaerobic fermentation by YEAST

the well studied eukaryotethe well studied eukaryote

Saccharomyces cerevisiaeSaccharomyces cerevisiae

study gene expression as a function of study gene expression as a function of timetime

for thousands of for thousands of genes genes simultaneouslysimultaneously

Egyptian relief tomb sculpture from 2400 BC – steps in the brewing of beer. Grain.

Known since at least 4000 Known since at least 4000 BC. Arose perhaps 8000 BCBC. Arose perhaps 8000 BC

CC66HH1212OO66 2C 2C22HH55OH + 2COOH + 2CO22

Saccharomyces Saccharomyces cerevisiaecerevisiae

Used in production Used in production of top-fermenting of top-fermenting alesales

anaerobic fermentation by anaerobic fermentation by YEASTYEAST led to the discovery of proteins (invertase) and their enzymatic led to the discovery of proteins (invertase) and their enzymatic

functionfunction

glucosglucosee

or fructose ethanoethanoll

invertase 2 2+

A good supply of sugar: nuclear DNA expresses invertase to catalyse FERMENTATIONFERMENTATION.

Otherwise, yeast turns on its mitochondrial DNA, to perform RESPIRATIONRESPIRATION

mitochondrmitochondrionion

Addition of the PO4

2-

phosphate group

nucleusnucleuswith DNAwith DNA

OO22-consuming-consuming phosphorylation phosphorylation (production of ATP from (production of ATP from ADP) in the inner ADP) in the inner membrane membrane

19 genes19 genes

~620~6200 0 genegeness

burnsburns available sources of carbon, including the alcohol

Diauxic (‘second life’) shift – Diauxic (‘second life’) shift – discovered by J. Monod in 1941: discovered by J. Monod in 1941: enzymes do not adaptenzymes do not adapt – other – other enzymes are expressed when enzymes are expressed when conditions change.conditions change.

ethanol

glucose

glycogen

trehalose

pH

cell number

Growth larger during Growth larger during fermentationfermentation

inside cellsinside cells

in milieuin milieu

Both the pH of the culture Both the pH of the culture and the cell numbers and the cell numbers oscillate: oscillate: cell division gets cell division gets in step, as well in step, as well

Metabolic oscillations in yeast Metabolic oscillations in yeast culturescultures Porro et al. 1988 6 h cycle6 h cycle

The cells go back and forth The cells go back and forth between consuming glucose between consuming glucose and producing ethanol and and producing ethanol and storing the glucose as storing the glucose as glycogen and trehalose. glycogen and trehalose.

respiratiorespirationn

fermentatifermentationonThe period of oscillations The period of oscillations

depends on the rate of sugar depends on the rate of sugar deliverydelivery

dissolved oxygen = - dissolved oxygen = - consumedconsumed

Raught, Gingras, Sonenberg 2001

Rohde, Heitman, Cardenas 2001

TwoTwo partially overlapping partially overlapping signaling pathwayssignaling pathways that that control this have been control this have been identified:identified:

protein kinase A (PKA)protein kinase A (PKA) & & target-of-rapamycin (TOR)target-of-rapamycin (TOR)

the two key proteins that the two key proteins that are expressed on the are expressed on the pathways. pathways.

Rapamycin a molecule (antibiotic) produced by bacteria Streptomyces hygroscopicus in the soil of Rapa Nui. Used e.g. to prevent rejection of kidney transplants

Mitochondria have to give a shout to the nucleus to make all the proteins that are involved in their structure and in breaking down sugars and performing oxidative phosphorylation.

TOR signals hunger: couples TOR signals hunger: couples nutrient availability with cell nutrient availability with cell growthgrowth

40 minute metabollic 40 minute metabollic oscillationsoscillations

Total of 6100 genes Total of 6100 genes expressed: 5329 expressed: 5329 nuclear & 19 nuclear & 19 mitochondrialmitochondrial

Klevecz, Bolen, Forrest, Murray (Yale) Klevecz, Bolen, Forrest, Murray (Yale) 20042004

650

2429

2250

RNA samples collected every 4 RNA samples collected every 4 min.min.

respiration

fermentation

A A genomewidgenomewide oscillatione oscillation

Mycoplasma genitalium – 470 genes – the smallest genome sustaining independent life was not studied

Genes involved in similar Genes involved in similar functions expressed in groups functions expressed in groups at the same timeat the same time

(another ~11 hour cycle: (another ~11 hour cycle: DeRisi, Iyer, Brown DeRisi, Iyer, Brown 1997)1997)

degradationconstruction of proteins and rRNA in ribosomes

Ubiquitin-Proteosom

Cytosolic Ribosomal

Sulfur&Methinine metabolism

Mitochondrial Ribosomal clustering

determined through correlations

Statistical clustering: guilt-by-associationStatistical clustering: guilt-by-association

“ “members of the same members of the same choir”choir”

Tu, Kudlicki, Rowicka, McKnight., Science 310:1152 (2005)

Ribosomal proteins

Mitochondrial proteins

DNA replication/cell

division

Energy metabolism Redox

homeostasis/sulfur metabolism

functionally interconnected groups of genes: proteins encoded by genes involved in the same biological process are often co-regulatedEisen, Spellman, Brown, Botstein 1998;

Saldanha, Brauer, Botstein 2004

300 min. cycle, ~6209 300 min. cycle, ~6209 genes, sampled every ~25 genes, sampled every ~25 minmin

Statistical tools – correlations - to detect Statistical tools – correlations - to detect significant differences in expression levels and significant differences in expression levels and identify groups of genes exhibiting similar identify groups of genes exhibiting similar expression patternsexpression patternsCorrelation measures do not provide direct Correlation measures do not provide direct insight into the identity or nature of the gene insight into the identity or nature of the gene interactions that give rise to the observed interactions that give rise to the observed expression patterns expression patterns

Violin players Violin players “express” in a “express” in a correlated way, but it correlated way, but it is the conductor that is the conductor that directs the directs the expressionexpression

WHO ARE THE WHO ARE THE CONDUCTORS CONDUCTORS IN THE IN THE GENETIC GENETIC NETWORKS?NETWORKS?

WHAT ARE THE EFFECTIVE GENE-GENE INTERACTIONS?

GG genes genesP<<GP<<G measurements of transcript levels measurements of transcript levelsGGxxPP data points data points GG((GG-1)/2 binary interaction values-1)/2 binary interaction values

INTERACTIONS MEDIATED BY PROTEINS

The challenge of direct network inference:What are the gene interactions that coordinate cellular changes in response to the environment?

The problem:

Under-determined

A variety of approaches to extract gene A variety of approaches to extract gene interactions: interactions: simple Boolean networks simple Boolean networks

Kauffman 1969, Liang, Fuhrman, Somogyi 1998; Akutsu, Miyano, Kuhara 2000; Shmulevich et al. 2002

Chen et al. 2000dynamical models of cellular processes dynamical models of cellular processes

Reverse engineering based on wiring rules for binary elements

Xi(t+1)=Fi [X1(t),…,XN(t)]

e.g. X1(t+1)=1 if X2(t) and X3(t) are 1

Fixed points and limit cyclesFixed points and limit cycles

dXi/dt=Fi [X1(t),…,XN(t),I]

dXi/dt= - Xi/τi + Σj Tijfj(Xj) + Σjk Tijk fj(Xj)fk(Xk) + Ii(t)

XXii gene product gene product concentrationconcentrationII noise, external input noise, external input

ffii sigmoidal regulation sigmoidal regulation functionfunctionττii degradation time degradation time

pairwispairwisee

tripletriple also spatially non-uniform

Guess the coupling constants

Bayesian network models Bayesian network models

graphical Gaussian models graphical Gaussian models

relevance networks relevance networks

Friedman 2004

Toh, Horimoto 2002; Schafer, Strimmer 2005

Butte, Kahane 2000

Probability for a gene transcript to be expressed at a given level is conditionally dependent on the expression levels of only a few other genes (its ‘parents’) – a directed network

Metrix reflecting functional relationships of genes. Pearson correlation coefficient above a treshold

Direct and indirect couplings in an undirected network based on ‘conditional independence’ between two genes; correlations

Equations for probabilities

‘‘Petri nets’, ‘process algebra’, ‘grammars’, ‘rule-based Petri nets’, ‘process algebra’, ‘grammars’, ‘rule-based formalism’formalism’

Efforts to constrain the model space by incorporating additional Efforts to constrain the model space by incorporating additional information from interventions and perturbations, other types information from interventions and perturbations, other types of molecular data, or literature mining are useful on a small of molecular data, or literature mining are useful on a small scalescale

Become unwieldy with increasing gene Become unwieldy with increasing gene numbers numbers

The principle of information entropy maximization to identify the most probable network

But myriad networks can reproduce the observed data with But myriad networks can reproduce the observed data with fidelityfidelity

SOLUTION:

PNAS 103, 19033-19038 PNAS 103, 19033-19038 (2006)(2006)

Jayanth R. Banavar Department of

Physics, Penn State University

Previous: PNAS 97 (2000) & 98 (2001) also with Holter and Mitra – fundamental modes in the temporal patterns of genetic expression

Nina Fedoroff Biology Dept. &

Huck Inst., Penn State

Univ. & Santa Fe Inst.

Amos Maritan Dipartimento di

Fisica, Universita di Padova, Italy

Timothy R. Lezon Penn

State University, now

UPitt.

The universal tendency for the amount of disorder in a system to increase

1865 – Clausius introduces concept of entropy for thermodynamics

1865 – Clausius introduces concept of entropy for thermodynamics

1877 – Boltzmann defines entropy in terms of probabilities, extending it to statistical mechanics

1877 – Boltzmann defines entropy in terms of probabilities, extending it to statistical mechanics

1948 – Shannon bases his theory of information on entropy

1948 – Shannon bases his theory of information on entropy

1957 - JaynesCurrent applications:Global climateNeural networksPlate tectonicsEcosystems

1957 - JaynesCurrent applications:Global climateNeural networksPlate tectonicsEcosystems

Entropy:

Entropy maximization Entropy maximization applied to gene expression dataapplied to gene expression data

G = Number of relevant degrees of freedom (“genes”)xi = Expression level of gene i

(The state of the genome in a given photograph)),...,( 1 Gxxx

x

xxS

)(ln)(

Probability of observing the state )(x x

Find the form of

)(x

that maximizes the system entropy:

Summation over various possible values of x

Constraints imposed by Lagrange multipliers

kj

P

k

ki

xjiji xxP

xxxxx

1

1)(

x

x

)(1

P

k

ki

xii xP

xxx1

1)(

Statistical inference with minimal reliance on the form of missing information

Most robust to experimental errors and noise in data

Use polished Use polished data:data:

XXii X Xii -<X -<Xii>>=0=0

P = Number of experiments (“photographs”)xi

k = Expression level of gene i in photograph k

M=C−1

The matrix of interactions is the pseudo-inverse of the correlation matrix

jijiij xxxxC

kj

P

k

kiji xx

Pxx

1

1

P

k

kii x

Px

1

1

xMxex

21

~)( M is the matrix of pair-wise interactions between genes

(higher order interactions determined perturbationally)

the polished data

GxG But only P data points on Cij

2 3 0

1 2 0

0 0 0

2 -3 0

-1 2 0

0 0 0

A=

A =

has no inverse

A A=1 0 0

0 1 0

0 0 0

BUT

where

-

-pseudoinverse

PSEUDOINVERSE MATRIX APSEUDOINVERSE MATRIX A-

For polished data y=x

If If P<GP<G, then , then CC is singular and has only is singular and has only P-P-

11 non-zero eigenvalues non-zero eigenvalues λλk k with the with the

eigenvector veigenvector vkk. . Pseudo-inverse Pseudo-inverse in the in the

non-zero eigenspacenon-zero eigenspace..

1

1

P

k k

kj

ki

ij

vvM

The gross, general correlations indicate little about the nature of the couplings between genes.

The eigenvectors with small eigenvalues dominate the calculation of M. These eigenvectors correspond to the residual fluctuations in expression levels that remain when the common, large-scale fluctuations are removed.

P-1

G

Negative MNegative Mij ij - excitory- excitoryThe change in the expression level of either The change in the expression level of either gene leads to a similar change in the othergene leads to a similar change in the other

Positive MPositive Mij ij - - inhibitoryinhibitory The change is oppositeThe change is opposite

Diagonal Mii – self-regulation

Nodes with large diagonal values generally have strong couplings with several other nodes

xMxex

21

~)( xMxex

21

~)( Hij = -JijSiSj

M is like a Hamiltonian

spin systems

Mij ~ -Jij

4670 genes4670 genes

582582

10081008

Switching from 582 to 1008 Switching from 582 to 1008 genes in the set leaves the Mgenes in the set leaves the Mijij largely intactlargely intact

Data on 5846 Data on 5846 genesgenes

19 of them 19 of them mitochondrialmitochondrial

Adding noise to the data

Robust to Robust to noisenoise

experimental level noise experimental level noise ~5~5

582: mean + standard deviation

Yeast chemostat cultures showing 40-min metabolic Yeast chemostat cultures showing 40-min metabolic oscillationsoscillations

Selecting the genes: highest profile varianceSelecting the genes: highest profile variance

Amino acid and protein synthesis

Peroxisomal anddegradative processes

Sulfur metabolism,redox homeostasis,stress response

Mitochondrial functionand biogenesis

Cell division,DNA synthesis,cytoskeleton

Nucleotide and RNA metabolism

Carbonmetabolism

Lipid metabolism

Other or unknown

The pairwise The pairwise interaction interaction

networknetwork

110 strongest interactions

582 582 genesgenes

Top 6 strongestThe hubs:

7

red <0

blue >0excitory

Amino acid and protein synthesisPerixomal and degradative processes

Sulfur metabolism, redox homeostasis, stress response

Nucleotide and RNA metabolism

Carbon metabolism

Lipid metabolism

Other or unknown

Mitochondrial function and biogenesisCell division, DNA synthesis, cytoskeleton

HFD1 – mitochondrial membrane protein – affects spindle pole body organizationFPR1 – part of TOR nutrient signaling pathway

BMH1 – regulates retrograde signaling from mitochondrion to nucleus – intersection between carbon and nitrogen

nutrient sensing

RPP1A – ribosomal stalk protein – under TOR regulation

CMD1 – calmodulin – involved in organization of actin cyto- skeleton, endocytosis and nuclear division

ARC15 – involved in assembly of actin-based cellular

structures – required for mitochondrial motility

during mitosisUTH1 – cell wall and mitochondrial outer membrane protein, involved in mitochondrial biogenesis and rapamycin resistance

Nutrient Signaling hubs: coordinating the nucleus and mitochondria

mitochondrial mitochondrial function and function and biogenesisbiogenesis

Amino acid and Amino acid and protein protein synthesissynthesis

Cell division, DNA Cell division, DNA synthesis, synthesis, cytoskeletoncytoskeleton

PKA

excitatoryexcitatoryinhibitoryinhibitory

Retrograde signaling

PKAPKA TORTOR FPR1FPR1

Bmh1Bmh1Rpp1ARpp1A

Ribosomebiogenesis

Uth1Uth1

Mitochondrialbiogenesis

Arc15Arc15 Mitochondrialmotility

Hfd1Hfd1

Cmd1Cmd1

Cytoskeletal dynamics

Translation Transcription Autophagy Cell division

retrograde retrograde signalingsignaling

(or back signalling)(or back signalling)

Nucleus Mitochondrion

in lysosomes

Glucoseregulation Mitochondrial

membrane

Nutrient Signaling Hubs: coordinating the nucleus and mitochondria

hubs

The The pairwise pairwise

interaction interaction networknetwork

Reveals more hubs, e.g. SNO1

Sno1 encodes a subunit of a glutaminase required for pyridoxine biosynthesis and its transcription is nutrient-regulated through the TOR pathway

1008 1008 genesgenes

The previously identified hubs, like BMH1, are still well connected

No HFD1 & CMD1No HFD1 & CMD1

Level 2: cellular infrastructureLevel 2: cellular infrastructure

Rim101Rim101

Cell wallpH regulationCell wallpH regulation

Pol30Pol30

DNA replication& repair, chromatinDNA replication& repair, chromatin

Pet18Pet18

MitochondrialmaintenanceMitochondrialmaintenance

Sphingolipid biosynthesis,Ca++ homeostasisSphingolipid biosynthesis,Ca++ homeostasis

Sur1Sur1

RNA synthesis,RNA polymerase IIRNA synthesis,RNA polymerase II

Rpb8Rpb8SnoISnoI

Pyridoxine biosynthesis,Enzyme cofactorsPyridoxine biosynthesis,Enzyme cofactors

Pbp4Pbp4

RNA synthesis,PolyadenylationRNA synthesis,Polyadenylation

Bmh1Bmh1

Cmd1Cmd1

Arc15Arc15

Hfd1Hfd1

NucleusNucleus MitochondrionMitochondrion

GlucoseregulationGlucose

regulation

Translation Transcription Autophagy Cell division Translation Transcription Autophagy Cell division

Cytoskeletal dynamics

Cytoskeletal dynamics

Mitochondrialmotility

Mitochondrialmotility

Uth1Uth1Rpp1ARpp1A

Retrograde signaling

Retrograde signaling

RibosomebiogenesisRibosomebiogenesis

Level I: nutrient signalingLevel I: nutrient signaling

PKAPKA TORTOR FPR1FPR1

Cellular Infrastructure Hubs

110 weakest 110 weakest interactionsinteractions

Disjoint – like for a Disjoint – like for a random networkrandom network

The contribution of two- and three-gene interactionsThe contribution of two- and three-gene interactions

triplets

pairs

all all genesgenes

3-body 3-body obtained obtained perturbativperturbativelyely

Small strenghts of the 3-body Small strenghts of the 3-body couplingscouplings

110 strongest interactions 110 strongest interactions inferred from the top 693 inferred from the top 693 genes in the genes in the long-period long-period dataset (5 h)dataset (5 h)

Overlaps between the major gene categoriesLong – 130 genes short - 102

Different networks (but correlations ~ the same)

The hub common in both The hub common in both networksnetworks

Rpp1A – ribosomalRpp1A – ribosomal

conclusionsconclusions

A method based on the principle of entropy A method based on the principle of entropy maximization to identify the gene interaction maximization to identify the gene interaction network with the highest probability of network with the highest probability of giving rise to experimentally observed giving rise to experimentally observed transcript profiles.transcript profiles.

Analysis of microarray data from genes Analysis of microarray data from genes in Saccharomyces cerevisiae identifies a in Saccharomyces cerevisiae identifies a gene interaction network that reflects gene interaction network that reflects the intracellular communication the intracellular communication pathways that adjust cellular metabolic pathways that adjust cellular metabolic activity and cell division to the limiting activity and cell division to the limiting nutrient conditions that trigger nutrient conditions that trigger metabolic oscillations.metabolic oscillations.

The method extracts meaningful The method extracts meaningful genetic connections and hubs in the genetic connections and hubs in the network.network.